![Evolution of cycles in a deforming granular material. (a) One can track a subset of particles and their corresponding contact network from a DEM simulation for increasing axial strain values $|\varepsilon_{22}|$. The system consists of 5098 spherical, polydisperse particles that were subjected to a quasistatic, biaxial compression test. At the smallest displayed axial strain, the set of particles in this figure yields a network that is composed of 3-cycles and 4-cycles. During loading, contacts are lost and longer cycles arise until only a single 9-cycle remains. (b) One way to quantify these structural changes is by calculating the global clustering coefficient $C$ (solid curve), which undergoes a sharp drop at peak stress, signifying the onset of material failure. (The dashed curve shows the standard deviation of the distribution of local clustering coefficients $C_{i}$). (c) A decrease in mean subgraph centrality $Y$ (solid curve) also illustrates the loss of short cycles during deformation. More specifically, the mean network bipartivity $R$ (dashed curve) increases with axial strain, highlighting that, during loading, closed walks of even (respectively, odd) length contribute more (respectively, less) to the mean subgraph centrality of the contact network. We adapted this figure, with permission, from [58].](https://oup.silverchair-cdn.com/oup/backfile/Content_public/Journal/comnet/6/4/10.1093_comnet_cny005/1/cny005f11.jpeg?Expires=1749776779&Signature=ICuL8lcIVtrcyq9qlTuF~EAPm2yfaKQf3hjdGXucYPxwCCUJvQQk4BLj88pPvbhME2xLAA9ga1DTy1e8~JNtvTbLeWxW~TRIeN7IrJXu8VsF7kSXYpa~BOwdeuKHTfJ3QhfpeitSaRyp9u22MHh2qt1av3lhnNeVvTQ050r1QvBPUmqn9UdhVhZOMyuPSIrWWfrLa9e8w9jGY~bGEjJS3VuEnaywoN5OdT5QNOt-6iLq0rmPJ7H150wMNgVQsE3rdt4vkOpp2voRtkf5BQuEuks5D4tvnRbuhStu1vOTVMp7h2BjFJqx8YDaD4blWlPkvMDwjQIkHmsGWrVn0I92uQ__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Evolution of cycles in a deforming granular material. (a) One can track a subset of particles and their corresponding contact network from a DEM simulation for increasing axial strain values |$|\varepsilon_{22}|$|. The system consists of 5098 spherical, polydisperse particles that were subjected to a quasistatic, biaxial compression test. At the smallest displayed axial strain, the set of particles in this figure yields a network that is composed of 3-cycles and 4-cycles. During loading, contacts are lost and longer cycles arise until only a single 9-cycle remains. (b) One way to quantify these structural changes is by calculating the global clustering coefficient |$C$| (solid curve), which undergoes a sharp drop at peak stress, signifying the onset of material failure. (The dashed curve shows the standard deviation of the distribution of local clustering coefficients |$C_{i}$|). (c) A decrease in mean subgraph centrality |$Y$| (solid curve) also illustrates the loss of short cycles during deformation. More specifically, the mean network bipartivity |$R$| (dashed curve) increases with axial strain, highlighting that, during loading, closed walks of even (respectively, odd) length contribute more (respectively, less) to the mean subgraph centrality of the contact network. We adapted this figure, with permission, from [58].
